From a previous answer of mine:

I should start by pointing out that the desire to "retake" North America was not a cause of the War of 1812. The war was declared by the United States against Great Britain, with the explicit aim of conquering Canada from the British to redress diplomatic grievances held by the United States against the UK. Those grievances included (but were not limited to):

1. The British practice of Impressment, by which captains of the Royal Navy were charged with re-capturing RN deserters, some of whom were American citizens
2. Efforts of British economic warfare aimed at Napoleon, including the "Orders in Council" which forbade foreign trade into French ports
3. British Indian Policy in Canada, which was popularly viewed as whipping up "savage frenzy" against American settlements

There were no plans to do anything with the United States, really, the British were fighting solely to defend Canada, not to conquer the United States.

While there were efforts to capture key cities - like New Orleans - to force a favorable end to the war, no one in the British government were keen to annex or somehow re-absorb the United States, at all. They were much more interested in ending the Napoleonic Wars and setting Europe to rights. The War of 1812 was considered a sideshow and little else.

I go into a little more detail in this previous answer on a similar question.